{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Asemic writing with Flat\n",
    "\n",
    "By [Allison Parrish](https://www.decontextualize.com/)\n",
    "\n",
    "This is a tutorial on how to use [flat](https://xxyxyz.org/flat), the random functions from [Numpy](http://www.numpy.org/) and [bezmerizing](https://github.com/aparrish/bezmerizing/) (a small library I made with simple functions for working with Bézier curves) to make various kinds of asemic writing.\n",
    "\n",
    "## Installation and preliminaries\n",
    "\n",
    "There are a number of Python libraries for drawing vector graphics, but [flat](https://xxyxyz.org/flat) is my favorite one to work with. It's small, powerful and elegant. It's also written in pure Python (i.e., does not need compiled code) and has no external dependencies, which makes it especially easy to install:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: flat in /Users/allison/Dropbox/projects/flat (0.3.1)\n",
      "\u001b[33mWARNING: You are using pip version 19.1.1, however version 20.0.2 is available.\n",
      "You should consider upgrading via the 'pip install --upgrade pip' command.\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "!pip install flat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial, I'm only using a subset of flat's functionality. The cell below imports the three functions from the library that I'm going to use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from flat import document, shape, rgba"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The flat library can export images in a handful of formats, including PNG. We can leverage this to \"embed\" the results of running flat code right into a Jupyter Notebook as we're working. The cell below creates a function `show()` that takes a flat `page` object, renders it as an SVG, and displays it in the notebook. I use this extensively below!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import SVG, display\n",
    "def show(page):\n",
    "    display(SVG(page.svg()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Bezmerizing](https://github.com/aparrish/bezmerizing/) is a small library I made with a handful of useful functions for working with Bézier curves, including a function for making smooth curved paths based on a list of points, and a function that can style such paths by adjusting their thickness along the path. Install it directly from GitHub like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting https://github.com/aparrish/bezmerizing/archive/master.zip\n",
      "  Downloading https://github.com/aparrish/bezmerizing/archive/master.zip\n",
      "\u001b[K     \\ 225kB 759kB/s\n",
      "  Requirement already satisfied (use --upgrade to upgrade): bezmerizing==0.0.2 from https://github.com/aparrish/bezmerizing/archive/master.zip in /Users/allison/anaconda/lib/python3.6/site-packages\n",
      "Requirement already satisfied: flat>=0.0.3 in /Users/allison/anaconda/lib/python3.6/site-packages (from bezmerizing==0.0.2)\n",
      "Requirement already satisfied: scipy>=1.1.0 in /Users/allison/anaconda/lib/python3.6/site-packages (from bezmerizing==0.0.2)\n",
      "\u001b[33mYou are using pip version 9.0.3, however version 18.1 is available.\n",
      "You should consider upgrading via the 'pip install --upgrade pip' command.\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "!pip install https://github.com/aparrish/bezmerizing/archive/master.zip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from bezmerizing import Polyline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assuming you're running this notebook with Anaconda, you probably already have Numpy installed. [Numpy](http://www.numpy.org/) is a widely-used Python library for math and statistics. I'm going to show you how to use a handful of functions from Numpy for generating random numbers. Use the cells below to import them into your notebook:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.random import uniform, normal, choice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Making shapes with flat\n",
    "\n",
    "Drawing with flat consists of a few steps:\n",
    "\n",
    "1. Create a document\n",
    "2. Add a page to the document\n",
    "3. Create shapes\n",
    "4. Place shapes on the page\n",
    "5. Display the page (or the document).\n",
    "\n",
    "A minimal example skips steps 3 and 4:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"283.4646pt\" version=\"1.1\" viewBox=\"0 0 283.4646 283.4646\" width=\"283.4646pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(100, 100, 'mm') # create a document 100mm x 100mm (can replace 'mm' with 'pt')\n",
    "page = d.addpage() # add a page\n",
    "show(page) # show the page"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "... but doesn't display anything. We've just made a blank page.\n",
    "\n",
    "To add a shape, create a `shape` object with the `shape()` function. The object returned from this function has methods that let you set the fill, stroke, and stroke width of the shape. Colors are specified with the `rgba()` function, which takes four parameters: the red, green, and blue components of the color (in the range 0—255), along with an alpha value (which controls how \"transparent\" the color will be—0 is completely transparent and 255 is completely opaque)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<flat.shape.shape at 0x1162997c8>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "figure = shape()\n",
    "figure.fill(rgba(255, 128, 255, 255))\n",
    "figure.stroke(rgba(128, 0, 255, 255))\n",
    "figure.width(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A `shape` object acts as a kind of container for a list of paths to draw with the fill and stroke you specified when you created the object. Add a rectangle to the shape with the `.rectangle()` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "rect = figure.rectangle(5, 5, 90, 90)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This creates a rectangle at position (5, 5) on the page with a width of 90 and a height of 90. ([See the documentation for a full list of shape methods and an explanation of what their parameters mean.](https://xxyxyz.org/flat))\n",
    "\n",
    "> Note for first-time programmers: Any word to the *left* of an equal sign (`=`) is called a *variable*. A \"variable\" takes the result of running some code and stores it for later under the name that you give it—sort of naming a file or putting a label on a folder. I used the word `rect` above to store the result of creating the `rectangle` shape, but you can use whatever word you want, as long as you use the same word when referring back to that value later. (There's nothing magical about calling it `rect`—I could have called is `lawrence` or `afkjsdhf`. Using `rect` just makes it easier to remember what I was using that variable for.\n",
    "\n",
    "To make this rectangle appear on the page, pass the value returned from the method to the `.place()` method of the page:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"283.4646pt\" version=\"1.1\" viewBox=\"0 0 283.4646 283.4646\" width=\"283.4646pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<rect fill=\"rgba(255,128,255,1)\" height=\"255.1181\" stroke=\"rgba(128,0,255,1)\" stroke-miterlimit=\"10\" stroke-width=\"4\" width=\"255.1181\" x=\"14.1732\" y=\"14.1732\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(100, 100, 'mm')\n",
    "page = d.addpage()\n",
    "page.place(rect)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nice! You'll notice that flat's coordinate system is set up such that the *upper left-hand corner* of the page is (0, 0). The X-axis increases as you move to the right of the page, while the Y-axes increases as you move *downwards*. (This is the opposite of how it works in a regular Cartesian coordinate system, but it's very common in computer graphics for some reason.)\n",
    "\n",
    "Because it's so common to set the fill, stroke and stroke width at once, flat supports a \"chained\" syntax so that you can set them all one one line. It looks like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "figure = shape().fill(rgba(255, 128, 255, 255)).stroke(rgba(128, 0, 255, 255)).width(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With all of this in mind, I put in the cell below all of the code necessary to draw the rectangle, from the creation of the document to displaying the page. Most of the rest of the examples in this tutorial will look like this, with all of the code to display a particular shape in the same cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"283.4646pt\" version=\"1.1\" viewBox=\"0 0 283.4646 283.4646\" width=\"283.4646pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<rect fill=\"rgba(255,128,255,1)\" height=\"255.1181\" stroke=\"rgba(128,0,255,1)\" stroke-miterlimit=\"10\" stroke-width=\"4\" width=\"255.1181\" x=\"14.1732\" y=\"14.1732\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(100, 100, 'mm')\n",
    "page = d.addpage()\n",
    "figure = shape().fill(rgba(255, 128, 255, 255)).stroke(rgba(128, 0, 255, 255)).width(4)\n",
    "rect = figure.rectangle(5, 5, 90, 90)\n",
    "page.place(rect)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To add another shape to the drawing, add a second call to a `shape` method. Another easy one to try out is `.circle()`, which draws a circle of a particular radius centered on the given (x, y) coordinate. Note that you have to call `page.place()` with all of the components of the shape you want to appear on in the drawing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"283.4646pt\" version=\"1.1\" viewBox=\"0 0 283.4646 283.4646\" width=\"283.4646pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<rect fill=\"rgba(255,128,255,1)\" height=\"255.1181\" stroke=\"rgba(128,0,255,1)\" stroke-miterlimit=\"10\" stroke-width=\"4\" width=\"255.1181\" x=\"14.1732\" y=\"14.1732\"/>\n",
       "<circle cx=\"93.5433\" cy=\"93.5433\" fill=\"rgba(255,128,255,1)\" r=\"70.8661\" stroke=\"rgba(128,0,255,1)\" stroke-miterlimit=\"10\" stroke-width=\"4\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(100, 100, 'mm')\n",
    "page = d.addpage()\n",
    "figure = shape().fill(rgba(255, 128, 255, 255)).stroke(rgba(128, 0, 255, 255)).width(4)\n",
    "rect = figure.rectangle(5, 5, 90, 90)\n",
    "circ = figure.circle(33, 33, 25)\n",
    "page.place(rect)\n",
    "page.place(circ)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want the circle to be a different color (or have a different stroke color or stroke width) from the rectangle, you need to create a second `shape` object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"283.4646pt\" version=\"1.1\" viewBox=\"0 0 283.4646 283.4646\" width=\"283.4646pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<rect fill=\"rgba(255,128,255,1)\" height=\"255.1181\" stroke=\"rgba(128,0,255,1)\" stroke-miterlimit=\"10\" stroke-width=\"4\" width=\"255.1181\" x=\"14.1732\" y=\"14.1732\"/>\n",
       "<circle cx=\"93.5433\" cy=\"93.5433\" fill=\"rgba(128,240,128,1)\" r=\"70.8661\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(100, 100, 'mm')\n",
    "page = d.addpage()\n",
    "# shape for rectangle\n",
    "figure = shape().fill(rgba(255, 128, 255, 255)).stroke(rgba(128, 0, 255, 255)).width(4)\n",
    "# shape for circle\n",
    "green_figure = shape().fill(rgba(128, 240, 128, 255)).nostroke()\n",
    "# add rectangle to figure\n",
    "rect = figure.rectangle(5, 5, 90, 90)\n",
    "# add circle to green figure\n",
    "circ = green_figure.circle(33, 33, 25)\n",
    "# place them both\n",
    "page.place(rect)\n",
    "page.place(circ)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that `.nostroke()` causes the shape to not have a stroke at all. Similarly, `.nofill()` will make the shape have no fill color.\n",
    "\n",
    "> Exercise ideas: Modify the cell above to change the coordinates and colors of the rectangle and circle. Add a new element to the drawing using a new shape that we haven't discussed yet (say, `ellipse` or `line`) using a stroke and fill different from the other shapes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Randomness with numpy\n",
    "\n",
    "For the purposes of this tutorial, let's think about asemic writing as a kind of random process. Our method of generating asemic writing with a computer will be to simulate the random movement of a hand holding a pen. The movement of the pen is constrained in certain ways—i.e., at any point in the process, some pen movements are more likely to happen than other pen movements. To model this process, we need a way to generate random numbers.\n",
    "\n",
    "Fortunately, the Numpy library has a wide variety of random number generators with different useful properties. Let's talk about a few of them.\n",
    "\n",
    "### Uniform distribution\n",
    "\n",
    "The `uniform()` function returns a number between 0 and 1, drawn from a \"uniform distribution.\" The word \"uniform\" here means that every value in the domain has *the same chance of being generated*—no number or range of numbers is more likely than any other. Run the cell below multiple times to see what happens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.27361543371694674"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "uniform()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using a `for` loop, you can generate a series of numbers to see what the distribution looks like. (You can change the number `8` to something larger to generate more numbers and better understand the distribution.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.07013100302448416\n",
      "0.1397809835134839\n",
      "0.21859138014353208\n",
      "0.15523595448827943\n",
      "0.5399525647207005\n",
      "0.474029472652012\n",
      "0.8353898318138343\n",
      "0.13836374892775738\n"
     ]
    }
   ],
   "source": [
    "for i in range(8):\n",
    "    print(uniform())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you give two parameters to `uniform()`, the function will evaluate to a number chosen from that range (with the first parameter being the low end of the range, and the second parameter being the high end.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.382456318776093\n",
      "-4.842943611271913\n",
      "-3.9090006054445423\n",
      "1.0648870287339545\n",
      "0.1642866508110883\n",
      "-1.6404369642354801\n",
      "4.993018223990802\n",
      "1.5414963500217693\n"
     ]
    }
   ],
   "source": [
    "for i in range(8):\n",
    "    print(uniform(-5, 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you need an integer instead of a floating-point number (i.e., a number with a decimal point), you can wrap the call to `uniform()` in a call to `int()`. The cell below simulates rolling a [twenty-sided die](https://en.wikipedia.org/wiki/Dice#Standard_variations):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "14\n",
      "14\n",
      "13\n",
      "8\n",
      "18\n",
      "9\n",
      "18\n",
      "2\n"
     ]
    }
   ],
   "source": [
    "for i in range(8):\n",
    "    print(int(uniform(20)+1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Exercise: Why do we need to add one to the result of the `uniform()` function in the example above?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normal distribution\n",
    "\n",
    "A random number generator with a normal distribution (also called the Gaussian distribution or the \"bell curve\") produces values mostly clustered around a particular number. When generating a random number with a normal distribution, you specify the \"center\" of the distribution (i.e., the number that the values will cluster around) and the value for the standard deviation of the distribution, which controls the \"spread\" of numbers returned, above and below the center. (~70% of numbers will be within this range; ~95% will be within double the range.) Generate a random number with a normal distribution using the `normal()` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.7815866604645137"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normal(0, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first parameter is the center, and the second is the standard deviation. (These are often called *mu* and *sigma*, respectively.) Run it a number of times and you should see that the numbers generated mostly cluster around the center:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.260375383727665\n",
      "-2.612857724868698\n",
      "2.3168879303138064\n",
      "0.2766363797317477\n",
      "-0.7014687478097344\n",
      "2.065597187506473\n",
      "-2.3444116252507725\n",
      "-3.9779891120220325\n"
     ]
    }
   ],
   "source": [
    "for i in range(8):\n",
    "    print(normal(0, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normal distributions are very useful in computer-generated art because they allow us to introduce and control variation, keeping values mostly in the same range.\n",
    "\n",
    "### Truncated normal distribution\n",
    "\n",
    "You may have noticed that sometimes the random number generator for the normal distribution produces values well outside the standard deviation. That's not a bug—it's just how normal distributions work. (In any data set, there are sometimes extreme outliers.)\n",
    "\n",
    "Nevertheless, in computer-generated art there's often a need to generate random numbers from a normal distribution that are *constrainted* to a particular range. (For example, you might want to generate a random color with a normal distribution, but never want your color values to fall outside of the range 0–255.) For this, you can use a *truncated normal distribution*. The following cell defines a function `t_normal()` to produce such values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import truncnorm\n",
    "def t_normal(a, b, mu, sigma):\n",
    "    tn = truncnorm((a-mu)/sigma, (b-mu)/sigma, loc=mu, scale=sigma)\n",
    "    return tn.rvs(1)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first parameter is the low end of the range, the second parameter is the high end, the third parameter is the center and the fourth parameter is the standard deviation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.64662445918368"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_normal(0, 255, 10, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choosing from a list with probabilities\n",
    "\n",
    "The `choice()` function implements a kind of *weighted* random choice, where you can set the weights randomly. The code in the cell below picks one of `50`, `100` or `150` (the values between the first set of brackets). It will pick these with 15% probability, 80% probability, and 5% probability respectively (as specified by the values between the second set of brackets)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "choice([50, 100, 150], p=[0.15, 0.8, 0.05])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calling this function multiple times should result in the specified distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100\n",
      "50\n",
      "100\n",
      "50\n",
      "100\n",
      "100\n",
      "100\n",
      "100\n"
     ]
    }
   ],
   "source": [
    "for i in range(8):\n",
    "    print(choice([50, 100, 150], p=[0.15, 0.8, 0.05]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Without the `p` parameter, the `choice()` function defaults to a uniform distribution (i.e., no result is more likely than any other):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100\n",
      "50\n",
      "50\n",
      "150\n",
      "50\n",
      "50\n",
      "150\n",
      "50\n"
     ]
    }
   ],
   "source": [
    "for i in range(8):\n",
    "    print(choice([50, 100, 150]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `sample()` function (from Python's standard `random` module) takes a list of values and returns the specified number of values, randomly selected (using a uniform distribution) from the list."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5, 10]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample([5, 10, 15, 20], 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing distributions with flat\n",
    "\n",
    "The code in the cell below places circles on a page with the (x, y) coordinates of their centers determined by different random distributions. The small red circles are uniformly distributed; the medium-sized green circles are normally distributed and the large blue circles are in a truncated normal distribution (centered on the center of the page, with the same spread.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
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       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(100, 100, 'mm')\n",
    "page = d.addpage()\n",
    "uniform_fig = shape().nostroke().stroke(rgba(255, 0, 0, 240)).width(1).nofill()\n",
    "normal_fig = shape().nostroke().stroke(rgba(64, 220, 64, 240)).width(1.5).nofill()\n",
    "t_normal_fig = shape().nostroke().stroke(rgba(0, 128, 255, 240)).width(2).nofill()\n",
    "mu = 50 # center of normal distributions\n",
    "sigma = 20 # standard deviation of normal distributions\n",
    "sample_n = 400 # number of \"samples\" (i.e. circles to draw for each distribution)\n",
    "for i in range(sample_n):\n",
    "    c = uniform_fig.circle(uniform(100), uniform(100), 1)\n",
    "    page.place(c)\n",
    "for i in range(sample_n):\n",
    "    c = normal_fig.circle(normal(mu, sigma), normal(mu, sigma), 1.5)\n",
    "    page.place(c)\n",
    "for i in range(sample_n):\n",
    "    c = t_normal_fig.circle(t_normal(20, 80, mu, sigma), t_normal(20, 80, mu, sigma), 2)\n",
    "    page.place(c)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Exercise: Copy the visualization above, but rewrite it to visualize three normal distributions with different standard deviations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random compositions\n",
    "\n",
    "The following code uses random numbers to set the stroke color, fill color, and position of a rectangle on the page. (Run it multiple times to see the results.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"283.4646pt\" version=\"1.1\" viewBox=\"0 0 283.4646 283.4646\" width=\"283.4646pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<rect fill=\"rgba(98,86,33,0.1569)\" height=\"71.7943\" stroke=\"rgba(61,61,95,1)\" stroke-miterlimit=\"10\" stroke-width=\"2.9788\" width=\"125.3862\" x=\"60.6352\" y=\"51.7899\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(100, 100, 'mm')\n",
    "page = d.addpage()\n",
    "stroke_c = rgba(int(t_normal(0, 100, 50, 25)),\n",
    "                int(t_normal(0, 100, 50, 25)),\n",
    "                int(uniform(255)),\n",
    "                255)\n",
    "fill_c = rgba(int(uniform(255)),\n",
    "              int(uniform(255)),\n",
    "              int(uniform(255)),\n",
    "              choice([40, 255], p=[0.9, 0.1]))\n",
    "figure = shape().stroke(stroke_c).fill(fill_c).width(uniform(5))\n",
    "rect = figure.rectangle(\n",
    "    normal(25, 10), normal(25, 10),\n",
    "    normal(50, 10), normal(20, 10))\n",
    "page.place(rect)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Play around with the parameters a bit until you understand how it works. Anywhere you see a call to `uniform()`, `normal()`, `t_normal()` or `choice()`, you can replace it with a call to another one of those same functions. (Note that colors values *always* have to be integers and always need to be between 0–255.)\n",
    "\n",
    "The cell below uses a `for` loop to draw multiple rectangles:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
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       "<title>Untitled</title>\n",
       "<rect fill=\"rgba(245,51,111,0.1569)\" height=\"-17.3817\" stroke=\"rgba(66,88,249,1)\" stroke-miterlimit=\"10\" stroke-width=\"2.4434\" width=\"189.872\" x=\"52.5669\" y=\"33.6167\"/>\n",
       "<rect fill=\"rgba(17,179,158,0.1569)\" height=\"76.9273\" stroke=\"rgba(4,38,58,1)\" stroke-miterlimit=\"10\" stroke-width=\"2.6922\" width=\"55.2224\" x=\"111.2975\" y=\"7.658\"/>\n",
       "<rect fill=\"rgba(249,121,6,0.1569)\" height=\"35.0912\" stroke=\"rgba(57,83,191,1)\" stroke-miterlimit=\"10\" stroke-width=\"3.8591\" width=\"177.4239\" x=\"52.046\" y=\"70.0222\"/>\n",
       "<rect fill=\"rgba(117,36,25,1)\" height=\"105.4734\" stroke=\"rgba(38,38,220,1)\" stroke-miterlimit=\"10\" stroke-width=\"3.39\" width=\"177.8839\" x=\"42.36\" y=\"86.5619\"/>\n",
       "<rect fill=\"rgba(171,153,244,0.1569)\" height=\"44.618\" stroke=\"rgba(5,55,130,1)\" stroke-miterlimit=\"10\" stroke-width=\"1.9388\" width=\"139.3267\" x=\"68.527\" y=\"54.7148\"/>\n",
       "<rect fill=\"rgba(83,218,96,0.1569)\" height=\"12.7065\" stroke=\"rgba(37,34,219,1)\" stroke-miterlimit=\"10\" stroke-width=\"4.1047\" width=\"179.3898\" x=\"109.4818\" y=\"70.8215\"/>\n",
       "<rect fill=\"rgba(107,92,128,0.1569)\" height=\"37.7674\" stroke=\"rgba(40,37,77,1)\" stroke-miterlimit=\"10\" stroke-width=\"2.5505\" width=\"155.1049\" x=\"8.44\" y=\"86.9257\"/>\n",
       "<rect fill=\"rgba(9,245,228,0.1569)\" height=\"52.7774\" stroke=\"rgba(33,47,191,1)\" stroke-miterlimit=\"10\" stroke-width=\"4.8377\" width=\"152.8443\" x=\"70.86\" y=\"86.5087\"/>\n",
       "<rect fill=\"rgba(120,153,15,0.1569)\" height=\"76.1592\" stroke=\"rgba(81,85,20,1)\" stroke-miterlimit=\"10\" stroke-width=\"3.6037\" width=\"188.1496\" x=\"16.1981\" y=\"44.352\"/>\n",
       "<rect fill=\"rgba(202,180,168,0.1569)\" height=\"23.044\" stroke=\"rgba(31,37,207,1)\" stroke-miterlimit=\"10\" stroke-width=\"2.5894\" width=\"175.4425\" x=\"162.4199\" y=\"64.7078\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(100, 100, 'mm')\n",
    "page = d.addpage()\n",
    "for i in range(int(uniform(8, 24))):\n",
    "    stroke_c = rgba(int(t_normal(0, 100, 50, 25)),\n",
    "                    int(t_normal(0, 100, 50, 25)),\n",
    "                    int(uniform(255)),\n",
    "                    255)\n",
    "    fill_c = rgba(int(uniform(255)),\n",
    "                  int(uniform(255)),\n",
    "                  int(uniform(255)),\n",
    "                  choice([40, 255], p=[0.9, 0.1]))\n",
    "    figure = shape().stroke(stroke_c).fill(fill_c).width(uniform(5))\n",
    "    rect = figure.rectangle(normal(25, 10), normal(25, 10),\n",
    "                            normal(50, 10), normal(20, 10))\n",
    "    page.place(rect)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's another example that uses circles instead of rectangles:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"283.4646pt\" version=\"1.1\" viewBox=\"0 0 283.4646 283.4646\" width=\"283.4646pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<circle cx=\"145.414\" cy=\"118.3923\" fill=\"rgba(0,0,94,0.3137)\" r=\"49.9232\"/>\n",
       "<circle cx=\"135.2574\" cy=\"141.5974\" fill=\"rgba(0,0,107,0.1569)\" r=\"41.5083\"/>\n",
       "<circle cx=\"159.7361\" cy=\"126.1235\" fill=\"rgba(0,0,217,0.3137)\" r=\"105.4564\"/>\n",
       "<circle cx=\"132.6857\" cy=\"156.2247\" fill=\"rgba(0,0,124,0.1569)\" r=\"77.2526\"/>\n",
       "<circle cx=\"107.3932\" cy=\"85.105\" fill=\"rgba(0,0,147,0.1569)\" r=\"68.6478\"/>\n",
       "<circle cx=\"93.6945\" cy=\"159.0106\" fill=\"rgba(0,0,46,0.1569)\" r=\"93.7643\"/>\n",
       "<circle cx=\"104.0277\" cy=\"142.5881\" fill=\"rgba(0,0,2,0.1569)\" r=\"62.3592\"/>\n",
       "<circle cx=\"113.035\" cy=\"163.6729\" fill=\"rgba(0,0,250,0.1569)\" r=\"83.47\"/>\n",
       "<circle cx=\"170.5601\" cy=\"195.0748\" fill=\"rgba(0,0,86,0.1569)\" r=\"64.4877\"/>\n",
       "<circle cx=\"134.8269\" cy=\"109.5034\" fill=\"rgba(0,0,174,0.3137)\" r=\"68.9817\"/>\n",
       "<circle cx=\"101.1571\" cy=\"122.6153\" fill=\"rgba(0,0,106,0.3137)\" r=\"82.8974\"/>\n",
       "<circle cx=\"165.4201\" cy=\"206.1843\" fill=\"rgba(0,0,254,0.1569)\" r=\"78.5299\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(100, 100, 'mm')\n",
    "page = d.addpage()\n",
    "for i in range(12):\n",
    "    fill_c = rgba(0, 0, int(uniform(255)), choice([40, 80], p=[0.5, 0.5]))\n",
    "    figure = shape().nostroke().fill(fill_c).width(np.random.uniform(5))\n",
    "    rect = figure.circle(normal(50, 10), normal(50, 10), t_normal(0, 100, 25, 15))\n",
    "    page.place(rect)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Exercise: Write code to generate random compositions by copying one of the cells above and modifying the parameters. Also try adding in new shapes or combining different kinds of shapes.\n",
    "\n",
    "> Exercise: Can you figure out how to make the \"page\" bigger? How do you need to adjust the parameters in the random number-generating functions to compensate?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Saving to disk\n",
    "\n",
    "If you make something with Flat that you really like, you can save it to disk for later use. You can do this in a number of ways, outputting to a number of formats. The `page` object's `.svg()` function returns a string of SVG:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "b'<?xml version=\"1.0\" encoding=\"UTF-8\"?>\\n<!-- Flat -->\\n<svg version=\"1.1\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"283.4646pt\" height=\"283.4646pt\" viewBox=\"0 0 283.4646 283.4646\">\\n<title>Untitled</title>\\n<circle cx=\"145.414\" cy=\"118.3923\" r=\"49.9232\" fill=\"rgba(0,0,94,0.3137)\" />\\n<circle cx=\"135.2574\" cy=\"141.5974\" r=\"41.5083\" fill=\"rgba(0,0,107,0.1569)\" />\\n<circle cx=\"159.7361\" cy=\"126.1235\" r=\"105.4564\" fill=\"rgba(0,0,217,0.3137)\" />\\n<circle cx=\"132.6857\" cy=\"156.2247\" r=\"77.2526\" fill=\"rgba(0,0,124,0.1569)\" />\\n<circle cx=\"107.3932\" cy=\"85.105\" r=\"68.6478\" fill=\"rgba(0,0,147,0.1569)\" />\\n<circle cx=\"93.6945\" cy=\"159.0106\" r=\"93.7643\" fill=\"rgba(0,0,46,0.1569)\" />\\n<circle cx=\"104.0277\" cy=\"142.5881\" r=\"62.3592\" fill=\"rgba(0,0,2,0.1569)\" />\\n<circle cx=\"113.035\" cy=\"163.6729\" r=\"83.47\" fill=\"rgba(0,0,250,0.1569)\" />\\n<circle cx=\"170.5601\" cy=\"195.0748\" r=\"64.4877\" fill=\"rgba(0,0,86,0.1569)\" />\\n<circle cx=\"134.8269\" cy=\"109.5034\" r=\"68.9817\" fill=\"rgba(0,0,174,0.3137)\" />\\n<circle cx=\"101.1571\" cy=\"122.6153\" r=\"82.8974\" fill=\"rgba(0,0,106,0.3137)\" />\\n<circle cx=\"165.4201\" cy=\"206.1843\" r=\"78.5299\" fill=\"rgba(0,0,254,0.1569)\" />\\n</svg>'"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "page.svg()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which you can then write to disk using the following code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"test.svg\", \"wb\") as fh:\n",
    "    fh.write(page.svg())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can open this SVG file with most vector editors (Inkscape, Illustrator, etc.), though note that if you use `rgba` colors, the file might not work in some editors.\n",
    "\n",
    "You can also save as an image using the `page` object's `.image()` method. For example, to save as a PNG:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"test.png\", \"wb\") as fh:\n",
    "    fh.write(page.image(ppi=72, kind=\"rgba\").png())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adjust the DPI with the `ppi` parameter. Note that Flat's PNG rasterizer is very slow, so preview at lower DPI before waiting for a higher-resolution render."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polylines\n",
    "\n",
    "Okay, so, random numbers are good! But how does this help us model pen strokes? Good question. We're getting there! The next step in our asemic journey is to create a *series of lines* linking a given list of points (specified as (x, y) coordinates). The name for this shape—a series of connected lines—is a *polyline*.\n",
    "\n",
    "The first step in making a polyline is to generate some points. The following cell creates a Python list with randomly-generated points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "pts = []\n",
    "for i in range(10):\n",
    "    pts.append([uniform(100), uniform(100)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the points look like. This is a data structure called a *list of lists* (i.e., a list that has other lists as its elements), which for various reasons is a convenient way to store polylines and polygons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[84.41756053729205, 71.34707731749896],\n",
       " [55.90706920616794, 40.70877644594958],\n",
       " [77.25654670014178, 2.391967004777115],\n",
       " [47.6659730813448, 19.460920035350185],\n",
       " [99.9857076018062, 61.55467559602252],\n",
       " [72.26972313458415, 10.447664935520635],\n",
       " [31.623566211403116, 34.7144306412098],\n",
       " [18.870564594653928, 41.22813760989996],\n",
       " [65.00297507918663, 19.55602668731524],\n",
       " [7.681729570278648, 35.863913922381144]]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's some code to draw the points on a page, using a circle to mark each point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"283.4646pt\" version=\"1.1\" viewBox=\"0 0 283.4646 283.4646\" width=\"283.4646pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<circle cx=\"239.2939\" cy=\"202.2437\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"158.4767\" cy=\"115.395\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"218.9949\" cy=\"6.7804\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"135.1161\" cy=\"55.1648\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"283.4241\" cy=\"174.4857\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"204.8591\" cy=\"29.6154\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"89.6416\" cy=\"98.4031\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"53.4914\" cy=\"116.8672\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"184.2604\" cy=\"55.4344\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"21.775\" cy=\"101.6615\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(100, 100, 'mm')\n",
    "page = d.addpage()\n",
    "figure = shape().stroke(rgba(0, 0, 0, 255)).width(1)\n",
    "for item in pts: # loop through the pts list, assigning each point to variable item\n",
    "    c = figure.circle(item[0], item[1], 2)\n",
    "    page.place(c)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The flat library has a built-in shape type, `.polyline()`, which draws lines connecting points. But the function wants the points as a list of points with the `x` and `y` coordinates directly following one another:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"283.4646pt\" version=\"1.1\" viewBox=\"0 0 283.4646 283.4646\" width=\"283.4646pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<polyline fill=\"none\" points=\"56.6929 28.3465 113.3858 212.5984 255.1181 240.9449 42.5197 42.5197\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(100, 100, 'mm')\n",
    "page = d.addpage()\n",
    "figure = shape().stroke(rgba(0, 0, 0, 255)).width(1)\n",
    "lines = figure.polyline([20, 10, 40, 75, 90, 85, 15, 15])\n",
    "page.place(lines)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get around this requirement of the library, the function below takes a list of lists and flattens it into a list (with the `x` and `y` components of the coordinates appropriately interleaved)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def flatten(t):\n",
    "    from itertools import chain\n",
    "    return list(chain(*t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code in the cell below draws a polyline from our randomly-generated points and draws circles where each point lies:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"283.4646pt\" version=\"1.1\" viewBox=\"0 0 283.4646 283.4646\" width=\"283.4646pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<polyline fill=\"none\" points=\"239.2939 202.2437 158.4767 115.395 218.9949 6.7804 135.1161 55.1648 283.4241 174.4857 204.8591 29.6154 89.6416 98.4031 53.4914 116.8672 184.2604 55.4344 21.775 101.6615\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"239.2939\" cy=\"202.2437\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"158.4767\" cy=\"115.395\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"218.9949\" cy=\"6.7804\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"135.1161\" cy=\"55.1648\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"283.4241\" cy=\"174.4857\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"204.8591\" cy=\"29.6154\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"89.6416\" cy=\"98.4031\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"53.4914\" cy=\"116.8672\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"184.2604\" cy=\"55.4344\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<circle cx=\"21.775\" cy=\"101.6615\" fill=\"none\" r=\"5.6693\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(100, 100, 'mm')\n",
    "page = d.addpage()\n",
    "figure = shape().stroke(rgba(0, 0, 0, 255)).width(1)\n",
    "lines = figure.polyline(flatten(pts))\n",
    "page.place(lines)\n",
    "for item in pts:\n",
    "    c = figure.circle(item[0], item[1], 2)\n",
    "    page.place(c)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Combining all of this in the same cell, and getting rid of the circles on the points, gives us some code that generates designs that *almost* look like alien glyphs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"283.4646pt\" version=\"1.1\" viewBox=\"0 0 283.4646 283.4646\" width=\"283.4646pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<polyline fill=\"none\" points=\"197.0756 181.9153 80.7311 90.0682 224.3039 95.5964 22.2223 89.6737 36.0959 110.3025 60.5481 142.7207 221.8432 267.547 280.1627 215.0017 151.7039 121.8403 270.7799 53.2669\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pts = []\n",
    "for i in range(10):\n",
    "    pts.append([uniform(100), uniform(100)])\n",
    "\n",
    "d = document(100, 100, 'mm')\n",
    "page = d.addpage()\n",
    "figure = shape().stroke(rgba(0, 0, 0, 255)).width(1)\n",
    "lines = figure.polyline(flatten(pts))\n",
    "page.place(lines)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polyline objects\n",
    "\n",
    "The `bezmerizing` library comes with a `Polyline` object that represents a polyline. It has a number of useful features that we'll get into below. To make a `Polyline` object, pass in a 2d list of points to the constructor like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {},
   "outputs": [],
   "source": [
    "pts = [[10, 10], [20, 20], [10, 30], [50, 65], [65, 25]]\n",
    "pline = Polyline(pts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To draw a `Polyline` object, pass it to Flat's `polyline` function. (Note that you don't need to use `flatten()` when working with `Polyline` objects!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"226.7717pt\" version=\"1.1\" viewBox=\"0 0 226.7717 226.7717\" width=\"226.7717pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<polyline fill=\"none\" points=\"28.3465 28.3465 56.6929 56.6929 28.3465 85.0394 141.7323 184.252 184.252 70.8661\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(80, 80, 'mm')\n",
    "page = d.addpage()\n",
    "figure = shape().stroke(rgba(0, 0, 0, 255)).width(1)\n",
    "lines = figure.polyline(pline)\n",
    "page.place(lines)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A `Polyline` object can also be used to draw a polygon with Flat's `.polygon()` method. (Essentially all this does is close the path.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"226.7717pt\" version=\"1.1\" viewBox=\"0 0 226.7717 226.7717\" width=\"226.7717pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<polygon fill=\"rgba(160,0,160,1)\" points=\"28.3465 28.3465 56.6929 56.6929 28.3465 85.0394 141.7323 184.252 184.252 70.8661\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(80, 80, 'mm')\n",
    "page = d.addpage()\n",
    "figure = shape().stroke(rgba(0, 0, 0, 255)).fill(rgba(160, 0, 160, 255)).width(1)\n",
    "lines = figure.polygon(pline)\n",
    "page.place(lines)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can examine a `Polyline`'s contents by evaluating it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Polyline([[10.0000, 10.0000], [20.0000, 20.0000], [10.0000, 30.0000], [50.0000, 65.0000], [65.0000, 25.0000]])"
      ]
     },
     "execution_count": 260,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And access the vertices directly (as a Numpy array) with the `.vertices` attribute:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10, 10],\n",
       "       [20, 20],\n",
       "       [10, 30],\n",
       "       [50, 65],\n",
       "       [65, 25]])"
      ]
     },
     "execution_count": 261,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pline.vertices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A `Polyline` object has `.translate()`, `.rotate()` and `.scale()` methods that operate similar to their equivalents in Processing. These methods apply the transformation to the vertices of the `Polyline` and return a new `Polyline` with the transformed vertices. For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Polyline([[20.0000, 20.0000], [40.0000, 40.0000], [20.0000, 60.0000], [100.0000, 130.0000], [130.0000, 50.0000]])"
      ]
     },
     "execution_count": 262,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pline.scale(2) # returns a new Polyline twice as big"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Polyline([[20.0000, 5.0000], [30.0000, 15.0000], [20.0000, 25.0000], [60.0000, 60.0000], [75.0000, 20.0000]])"
      ]
     },
     "execution_count": 263,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pline.translate(10, -5) # returns a new Polyline translated up and to the left"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Polyline([[14.1421, 0.0000], [28.2843, 0.0000], [28.2843, 14.1421], [81.3173, 10.6066], [63.6396, -28.2843]])"
      ]
     },
     "execution_count": 264,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pline.rotate(np.pi*0.25) # rotates the polyline pi/4 radians"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This makes it possible to write a bit of code that produces polylines like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "metadata": {},
   "outputs": [],
   "source": [
    "pts = []\n",
    "for i in range(12):\n",
    "    pts.append([normal(), normal()])\n",
    "pline = Polyline(pts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then draw the same polyline in multiple ways and in multiple places."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"283.4646pt\" version=\"1.1\" viewBox=\"0 0 283.4646 283.4646\" width=\"283.4646pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<polyline fill=\"none\" points=\"139.0928 132.2194 101.2249 114.2567 161.612 160.6622 152.8701 163.4364 134.9975 193.9486 149.2023 107.799 145.6434 164.7951 115.8829 100.8338 157.7208 133.6768 153.5157 193.275 156.6613 169.2091 108.8556 152.7886\" stroke=\"rgba(0,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"51.8403 76.1451 15.9149 151.881 108.7261 31.1068 114.2744 48.5906 175.2988 84.3357 2.9995 55.926 116.9918 63.044 -10.9308 122.5648 54.7553 38.889 173.9516 47.2992 125.8198 41.0082 92.9788 136.6196\" stroke=\"rgba(128,0,128,1)\" stroke-miterlimit=\"10\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"214.6589 178.0823 199.9566 171.1083 223.4021 189.1254 220.008 190.2025 213.0689 202.0489 218.584 168.601 217.2022 190.73 205.6476 165.8968 221.8913 178.6482 220.2587 201.7874 221.48 192.4437 202.9192 186.0684\" stroke=\"rgba(0,128,128,1)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"170.1757 212.6479 155.5884 205.7284 178.8504 223.6045 175.4829 224.6732 168.5981 236.4269 174.07 203.2408 172.699 225.1965 161.2349 200.5577 177.3514 213.2093 175.7316 236.1674 176.9433 226.8969 158.5278 220.5715\" stroke=\"rgba(0,128,128,1)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"282.675 220.9215 273.63 216.631 288.0538 227.7152 285.9658 228.3778 281.6968 235.6659 285.0897 215.0885 284.2396 228.7024 277.1312 213.4248 287.1244 221.2696 286.12 235.505 286.8713 229.7567 275.4526 225.8346\" stroke=\"rgba(0,128,128,1)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"277.8455 222.5074 265.9667 216.8726 284.9096 231.4296 282.1673 232.2999 276.5609 241.8713 281.0168 214.8469 279.9004 232.7261 270.5648 212.662 283.689 222.9646 282.3699 241.66 283.3566 234.1107 268.3604 228.9598\" stroke=\"rgba(0,128,128,1)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"213.5002 200.5748 203.3054 195.7389 219.5629 208.2323 217.2094 208.9791 212.3977 217.1937 216.2219 194.0003 215.2638 209.3449 207.2517 192.1252 218.5153 200.9672 217.3832 217.0123 218.23 210.5333 205.3597 206.1125\" stroke=\"rgba(0,128,128,1)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"151.9271 266.8967 141.8472 262.1153 157.9213 274.4677 155.5944 275.2062 150.837 283.328 154.6181 260.3963 153.6707 275.5678 145.749 258.5423 156.8856 267.2846 155.7663 283.1487 156.6035 276.7428 143.8784 272.3719\" stroke=\"rgba(0,128,128,1)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"211.2314 213.4018 196.2446 206.2927 220.1437 224.6585 216.6839 225.7564 209.6106 237.832 215.2324 203.737 213.8239 226.2941 202.0457 200.9804 218.6037 213.9786 216.9395 237.5655 218.1844 228.041 199.2645 221.5423\" stroke=\"rgba(0,128,128,1)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"263.8721 141.7878 249.9605 135.1888 272.145 152.237 268.9335 153.2561 262.3676 164.4654 267.5861 132.8165 266.2786 153.7553 255.3455 130.2577 270.7155 142.3233 269.1707 164.218 270.3263 155.3768 252.7638 149.3444\" stroke=\"rgba(0,128,128,1)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"245.2616 253.5368 233.2236 247.8265 252.4203 262.5786 249.6413 263.4605 243.9597 273.1602 248.4754 245.7736 247.344 263.8924 237.8833 243.5595 251.1834 254.0001 249.8466 272.946 250.8465 265.2956 235.6493 260.0756\" stroke=\"rgba(0,128,128,1)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"225.5858 248.9219 214.8308 243.8203 231.9816 257.0001 229.4987 257.788 224.4227 266.4539 228.457 241.9862 227.4463 258.1739 218.9939 240.008 230.8764 249.3359 229.6821 266.2626 230.5755 259.4275 216.998 254.7639\" stroke=\"rgba(0,128,128,1)\" stroke-miterlimit=\"10\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(100, 100, 'mm')\n",
    "page = d.addpage()\n",
    "figure = shape().stroke(rgba(0, 0, 0, 255)).width(1)\n",
    "figure2 = shape().stroke(rgba(128, 0, 128, 255)).width(2)\n",
    "figure3 = shape().stroke(rgba(0, 128, 128, 255)).width(1)\n",
    "# ten times bigger, at 50, 50\n",
    "page.place(\n",
    "    figure.polyline(pline.scale(10).translate(50, 50)))\n",
    "# rotated\n",
    "page.place(\n",
    "    figure2.polyline(pline.scale(20).rotate(np.pi*0.5).translate(25, 25)))\n",
    "# many small copies\n",
    "for i in range(10):\n",
    "    page.place(figure3.polyline(\n",
    "        pline.scale(uniform(2, 4)).translate(uniform(50, 100), uniform(50, 100))))\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you have other transformations in mind, you can always manipulate a Polyline's `.vertices` array directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"283.4646pt\" version=\"1.1\" viewBox=\"0 0 283.4646 283.4646\" width=\"283.4646pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<polyline fill=\"none\" points=\"140.305 91.8416 130.0225 124.3231 114.5241 186.7286 106.6984 121.4402 202.035 152.3038 102.6261 114.1588 131.6968 90.8276 141.88 184.4554 119.5986 150.2258 161.775 154.9573 149.0856 134.4241 173.9983 121.932\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"141.7712 100.7882 131.4886 133.2697 115.9903 195.6752 108.1646 130.3868 203.5011 161.2503 104.0922 123.1054 133.163 99.7742 143.3461 193.4019 121.0648 159.1723 163.2411 163.9038 150.5518 143.3707 175.4644 130.8785\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"144.0854 101.8458 133.8028 134.3273 118.3045 196.7328 110.4787 131.4444 205.8153 162.3079 106.4064 124.163 135.4772 100.8318 145.6603 194.4596 123.379 160.2299 165.5553 164.9615 152.8659 144.4283 177.7786 131.9361\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"143.1445 101.2637 132.8619 133.7452 117.3636 196.1507 109.5378 130.8623 204.8744 161.7258 105.4655 123.5809 134.5363 100.2497 144.7194 193.8774 122.4381 159.6478 164.6144 164.3793 151.925 143.8462 176.8377 131.354\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"142.074 107.1359 131.7914 139.6174 116.2931 202.0228 108.4673 136.7345 203.8039 167.598 104.395 129.4531 133.4658 106.1218 143.6489 199.7496 121.3676 165.52 163.5439 170.2515 150.8545 149.7184 175.7672 137.2262\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"143.6135 108.8954 133.3309 141.3769 117.8326 203.7824 110.0069 138.494 205.3434 169.3576 105.9345 131.2126 135.0053 107.8814 145.1885 201.5092 122.9071 167.2795 165.0835 172.0111 152.3941 151.4779 177.3067 138.9857\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"146.6414 108.2759 136.3588 140.7574 120.8605 203.1629 113.0348 137.8745 208.3713 168.738 108.9624 130.5931 138.0332 107.2619 148.2164 200.8896 125.935 166.66 168.1114 171.3915 155.422 150.8584 180.3346 138.3662\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"148.4529 112.3244 138.1703 144.8059 122.672 207.2114 114.8463 141.923 210.1828 172.7865 110.7739 134.6416 139.8447 111.3104 150.0279 204.9382 127.7465 170.7085 169.9229 175.4401 157.2335 154.9069 182.1461 142.4147\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"147.3175 107.8033 137.0349 140.2848 121.5366 202.6902 113.7108 137.4019 209.0474 168.2654 109.6385 130.1205 138.7093 106.7892 148.8924 200.417 126.6111 166.1874 168.7874 170.9189 156.098 150.3858 181.0107 137.8936\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"148.021 107.7741 137.7384 140.2556 122.2401 202.661 114.4144 137.3727 209.7509 168.2362 110.342 130.0913 139.4128 106.76 149.596 200.3878 127.3146 166.1582 169.491 170.8897 156.8016 150.3566 181.7142 137.8644\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"148.9224 102.5057 138.6398 134.9872 123.1415 197.3927 115.3157 132.1043 210.6523 162.9679 111.2434 124.8229 140.3142 101.4917 150.4973 195.1195 128.216 160.8898 170.3923 165.6214 157.7029 145.0882 182.6156 132.5961\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"149.4046 104.1184 139.1221 136.5999 123.6237 199.0053 115.798 133.717 211.1346 164.5805 111.7257 126.4356 140.7964 103.1044 150.9796 196.7321 128.6982 162.5025 170.8746 167.234 158.1852 146.7009 183.0979 134.2087\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"153.1099 107.9501 142.8273 140.4315 127.329 202.837 119.5033 137.5487 214.8398 168.4122 115.4309 130.2672 144.5017 106.936 154.6848 200.5638 132.4035 166.3342 174.5798 171.0657 161.8905 150.5326 186.8031 138.0404\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"155.1337 107.7552 144.8511 140.2367 129.3528 202.6422 121.527 137.3538 216.8636 168.2173 117.4547 130.0724 146.5255 106.7412 156.7086 200.369 134.4272 166.1393 176.6036 170.8709 163.9142 150.3377 188.8269 137.8455\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"158.0538 110.2473 147.7712 142.7288 132.2729 205.1343 124.4472 139.846 219.7837 170.7095 120.3748 132.5645 149.4456 109.2333 159.6287 202.8611 137.3474 168.6315 179.5237 173.363 166.8344 152.8298 191.747 140.3377\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"159.7724 110.4073 149.4898 142.8888 133.9915 205.2942 126.1658 140.0059 221.5023 170.8694 122.0934 132.7245 151.1642 109.3932 161.3474 203.021 139.066 168.7914 181.2424 173.5229 168.553 152.9898 193.4656 140.4976\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"157.7724 117.7735 147.4898 150.255 131.9915 212.6605 124.1658 147.3721 219.5023 178.2357 120.0934 140.0907 149.1642 116.7595 159.3474 210.3873 137.066 176.1576 179.2424 180.8892 166.553 160.356 191.4656 147.8638\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"151.9684 117.728 141.6858 150.2094 126.1875 212.6149 118.3618 147.3266 213.6983 178.1901 114.2894 140.0451 143.3602 116.7139 153.5434 210.3417 131.262 176.1121 173.4384 180.8436 160.749 160.3105 185.6616 147.8183\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"150.1189 115.2242 139.8364 147.7057 124.338 210.1112 116.5123 144.8228 211.8488 175.6864 112.4399 137.5414 141.5107 114.2102 151.6939 207.838 129.4125 173.6083 171.5889 178.3399 158.8995 157.8067 183.8122 145.3146\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"149.1981 117.101 138.9155 149.5824 123.4172 211.9879 115.5915 146.6996 210.928 177.5631 111.5191 139.4181 140.5899 116.0869 150.773 209.7147 128.4917 175.4851 170.6681 180.2166 157.9787 159.6835 182.8913 147.1913\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"152.278 115.7844 141.9954 148.2659 126.4971 210.6714 118.6713 145.3831 214.0079 176.2466 114.599 138.1016 143.6698 114.7704 153.8529 208.3982 131.5716 174.1686 173.7479 178.9001 161.0585 158.3669 185.9712 145.8748\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"154.7149 119.0559 144.4323 151.5374 128.934 213.9429 121.1083 148.6546 216.4448 179.5181 117.0359 141.3731 146.1067 118.0419 156.2899 211.6697 134.0085 177.4401 176.1849 182.1716 163.4955 161.6384 188.4081 149.1463\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
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       "<polyline fill=\"none\" points=\"162.6478 133.1777 152.3652 165.6592 136.8669 228.0646 129.0411 162.7763 224.3777 193.6398 124.9688 155.4949 154.0396 132.1636 164.2227 225.7914 141.9414 191.5618 184.1177 196.2933 171.4283 175.7602 196.341 163.268\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"156.2934 129.117 146.0108 161.5985 130.5125 224.0039 122.6867 158.7156 218.0233 189.5791 118.6144 151.4342 147.6852 128.103 157.8683 221.7307 135.587 187.5011 177.7633 192.2326 165.0739 171.6995 189.9866 159.2073\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"158.044 131.0706 147.7614 163.5521 132.2631 225.9576 124.4373 160.6692 219.7739 191.5328 120.365 153.3878 149.4358 130.0566 159.6189 223.6844 137.3375 189.4547 179.5139 194.1863 166.8245 173.6531 191.7372 161.161\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"158.5021 131.6287 148.2195 164.1102 132.7212 226.5157 124.8955 161.2273 220.232 192.0908 120.8231 153.9459 149.8939 130.6147 160.0771 224.2424 137.7957 190.0128 179.9721 194.7443 167.2827 174.2112 192.1953 161.719\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"157.4901 135.2108 147.2075 167.6922 131.7092 230.0977 123.8834 164.8094 219.22 195.6729 119.8111 157.5279 148.8819 134.1967 159.065 227.8245 136.7837 193.5949 178.96 198.3264 166.2706 177.7933 191.1833 165.3011\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"159.9512 139.5041 149.6686 171.9856 134.1703 234.3911 126.3445 169.1027 221.6811 199.9663 122.2722 161.8213 151.343 138.4901 161.5261 232.1179 139.2447 197.8883 181.4211 202.6198 168.7317 182.0866 193.6444 169.5945\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"165.2153 142.949 154.9327 175.4305 139.4344 237.836 131.6087 172.5476 226.9452 203.4112 127.5363 165.2662 156.6071 141.935 166.7903 235.5628 144.5089 201.3331 186.6853 206.0647 173.9959 185.5315 198.9085 173.0393\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"159.8187 141.5054 149.5361 173.9869 134.0378 236.3924 126.2121 171.104 221.5486 201.9675 122.1397 163.8226 151.2105 140.4914 161.3937 234.1191 139.1123 199.8895 181.2887 204.6211 168.5993 184.0879 193.5119 171.5957\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"153.7734 138.8365 143.4908 171.3179 127.9925 233.7234 120.1668 168.4351 215.5033 199.2986 116.0944 161.1536 145.1652 137.8224 155.3484 231.4502 133.067 197.2206 175.2434 201.9521 162.554 181.419 187.4666 168.9268\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"152.8181 137.957 142.5355 170.4385 127.0372 232.844 119.2115 167.5557 214.548 198.4192 115.1391 160.2742 144.2099 136.943 154.3931 230.5708 132.1117 196.3412 174.2881 201.0727 161.5987 180.5395 186.5113 168.0474\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"153.1587 135.5374 142.8761 168.0188 127.3778 230.4243 119.5521 165.136 214.8886 195.9995 115.4797 157.8545 144.5505 134.5233 154.7337 228.1511 132.4523 193.9215 174.6287 198.653 161.9393 178.1199 186.8519 165.6277\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"155.1108 138.3183 144.8283 170.7998 129.3299 233.2052 121.5042 167.9169 216.8407 198.7804 117.4318 160.6355 146.5026 137.3042 156.6858 230.932 134.4044 196.7024 176.5808 201.4339 163.8914 180.9008 188.8041 168.4086\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"155.6347 137.6041 145.3521 170.0856 129.8538 232.491 122.028 167.2027 217.3646 198.0662 117.9557 159.9213 147.0265 136.5901 157.2096 230.2178 134.9283 195.9882 177.1046 200.7197 164.4152 180.1866 189.3279 167.6944\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"151.6085 135.6147 141.3259 168.0962 125.8276 230.5016 118.0018 165.2133 213.3384 196.0768 113.9295 157.9319 143.0003 134.6006 153.1834 228.2284 130.9021 193.9988 173.0784 198.7303 160.389 178.1972 185.3017 165.705\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"152.4733 133.4064 142.1907 165.8878 126.6924 228.2933 118.8666 163.005 214.2032 193.8685 114.7943 155.7235 143.8651 132.3923 154.0482 226.0201 131.7669 191.7905 173.9432 196.522 161.2538 175.9889 186.1665 163.4967\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"147.8537 129.6571 137.5711 162.1386 122.0728 224.544 114.2471 159.2557 209.5836 190.1192 110.1747 151.9743 139.2455 128.643 149.4286 222.2708 127.1473 188.0412 169.3236 192.7727 156.6343 172.2396 181.5469 159.7474\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"149.2171 132.5073 138.9345 164.9888 123.4362 227.3943 115.6105 162.1059 210.947 192.9695 111.5381 154.8245 140.6089 131.4933 150.7921 225.1211 128.5107 190.8914 170.6871 195.623 157.9977 175.0898 182.9103 162.5976\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"145.4753 134.9745 135.1927 167.456 119.6944 229.8615 111.8687 164.5731 207.2052 195.4366 107.7963 157.2917 136.8671 133.9605 147.0503 227.5882 124.7689 193.3586 166.9453 198.0901 154.2559 177.557 179.1685 165.0648\" stroke=\"rgba(0,0,0,0.0941)\" stroke-miterlimit=\"10\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate polyline\n",
    "pts = []\n",
    "for i in range(12):\n",
    "    pts.append([normal(), normal()])\n",
    "pline = Polyline(pts)\n",
    "\n",
    "# draw polyline many times on top of itself\n",
    "d = document(100, 100, 'mm')\n",
    "page = d.addpage()\n",
    "figure = shape().stroke(rgba(0, 0, 0, 24)).width(1)\n",
    "for i in range(100):\n",
    "    # add a bit of noise to the coordinates on each loop\n",
    "    pline.vertices += np.random.randn(2) * 0.1\n",
    "    lines = figure.polyline(pline.scale(10).translate(50, 50))\n",
    "    page.place(lines)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polylines on a grid\n",
    "\n",
    "Let's pursue this aesthetic a little bit further. Introducing further constraints to the randomness will result in designs that give the impression of conforming to an underlying system (and, let's hypothesize, thereby give an impression of being more like \"writing\"). The code below also uses random polylines, but constrains the polylines to begin and end on certain points in the grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 268,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"283.4646pt\" version=\"1.1\" viewBox=\"0 0 283.4646 283.4646\" width=\"283.4646pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<polyline fill=\"none\" points=\"269.2913 269.2913 141.7323 269.2913 269.2913 141.7323 14.1732 269.2913 14.1732 269.2913 269.2913 269.2913 14.1732 141.7323 14.1732 141.7323 14.1732 14.1732 14.1732 269.2913 14.1732 14.1732 269.2913 269.2913\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"4\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(100, 100, 'mm')\n",
    "page = d.addpage()\n",
    "figure = shape().stroke(rgba(0, 0, 0, 255)).width(4).join('round')\n",
    "pts = []\n",
    "for i in range(12):\n",
    "    x = choice([0, 0.5, 1])\n",
    "    y = choice([0, 0.5, 1])\n",
    "    pts.append([x, y])\n",
    "pline = Polyline(pts)\n",
    "lines = figure.polyline(pline.scale(90).translate(5, 5))\n",
    "page.place(lines)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The key bit of code here is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 269,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "choice([0, 0.5, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "... which is a Python expression that returns one of `0`, `0.5`, and `1` (at random). Using this expression for both the `x` and `y` coordinate of each point on the polyline leads to a result wherein each polyline randomly connects one of nine points on a grid. The `.scale()` and `.translate()` methods scale this polyline up and move it to the appropriate place on the screen (i.e., scaled up to 90 units, moved 5 units from the side just to give it a little border).\n",
    "\n",
    "The cell below defines a function, `make_char()`, that generates a series of points using a more general version of this expression. It adds four to twelve segments to the polyline (randomly determined)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_char():\n",
    "    pts = []\n",
    "    for i in range(int(t_normal(4, 12, 8, 2))):\n",
    "        x = (choice([0, 0.5, 1]))\n",
    "        y = (choice([0, 0.5, 1]))\n",
    "        pts.append([x, y])\n",
    "    return Polyline(pts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results of the `make_char()` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Polyline([[1.0000, 0.0000], [1.0000, 0.0000], [0.5000, 0.5000], [1.0000, 0.0000], [1.0000, 0.0000], [0.5000, 0.0000], [0.5000, 0.0000], [0.0000, 0.0000]])"
      ]
     },
     "execution_count": 271,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "make_char()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following cell draws these \"characters\" on a grid, so we can see many variations at once:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"425.1969pt\" version=\"1.1\" viewBox=\"0 0 425.1969 425.1969\" width=\"425.1969pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<polyline fill=\"none\" points=\"8.5039 8.5039 44.1142 44.1142 8.5039 26.3091 8.5039 26.3091 26.3091 8.5039 8.5039 44.1142 44.1142 44.1142 26.3091 26.3091 44.1142 44.1142\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"26.3091 61.6535 44.1142 97.2638 44.1142 97.2638 8.5039 61.6535\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"26.3091 114.8031 26.3091 114.8031 8.5039 150.4134 44.1142 150.4134 8.5039 132.6083 26.3091 114.8031 44.1142 150.4134 26.3091 132.6083 26.3091 132.6083 44.1142 132.6083\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"26.3091 203.563 8.5039 167.9528 26.3091 185.7579 26.3091 185.7579 8.5039 185.7579 26.3091 167.9528 44.1142 203.563 26.3091 185.7579 26.3091 167.9528\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"44.1142 238.9075 8.5039 221.1024 44.1142 256.7126 26.3091 221.1024 26.3091 238.9075 26.3091 256.7126 44.1142 238.9075\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"26.3091 274.252 26.3091 309.8622 8.5039 309.8622 44.1142 274.252 8.5039 309.8622 8.5039 274.252\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"44.1142 327.4016 44.1142 327.4016 44.1142 327.4016 44.1142 363.0118 8.5039 327.4016 8.5039 327.4016 8.5039 327.4016 8.5039 327.4016\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"44.1142 398.3563 44.1142 398.3563 44.1142 398.3563 26.3091 398.3563 8.5039 416.1614 44.1142 416.1614 26.3091 398.3563 26.3091 398.3563 8.5039 398.3563\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"79.4587 8.5039 61.6535 44.1142 79.4587 44.1142 79.4587 8.5039 79.4587 26.3091 61.6535 44.1142 97.2638 8.5039\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"97.2638 61.6535 61.6535 97.2638 61.6535 79.4587 97.2638 97.2638 61.6535 97.2638 61.6535 97.2638 97.2638 61.6535 79.4587 97.2638 97.2638 97.2638\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"97.2638 150.4134 97.2638 150.4134 61.6535 132.6083 61.6535 114.8031 61.6535 150.4134 97.2638 132.6083 61.6535 132.6083\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"79.4587 185.7579 61.6535 167.9528 97.2638 203.563 97.2638 203.563\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"61.6535 238.9075 97.2638 256.7126 79.4587 256.7126 79.4587 238.9075 97.2638 256.7126 79.4587 238.9075 79.4587 221.1024\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
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       "<polyline fill=\"none\" points=\"150.4134 114.8031 114.8031 150.4134 114.8031 114.8031 150.4134 150.4134 114.8031 114.8031 150.4134 114.8031 132.6083 132.6083 114.8031 114.8031 114.8031 114.8031 114.8031 132.6083\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"132.6083 185.7579 132.6083 167.9528 114.8031 167.9528 150.4134 185.7579 150.4134 167.9528 114.8031 167.9528 150.4134 185.7579 114.8031 203.563 114.8031 203.563 132.6083 167.9528\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"132.6083 256.7126 132.6083 238.9075 114.8031 256.7126 150.4134 256.7126 114.8031 256.7126\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"114.8031 309.8622 114.8031 292.0571 132.6083 309.8622 132.6083 292.0571 150.4134 274.252\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"132.6083 363.0118 132.6083 363.0118 150.4134 345.2067 150.4134 363.0118 150.4134 327.4016 150.4134 327.4016 150.4134 363.0118 150.4134 345.2067\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
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       "<polyline fill=\"none\" points=\"238.9075 26.3091 256.7126 44.1142 221.1024 26.3091 256.7126 44.1142 221.1024 26.3091\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
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       "<polyline fill=\"none\" points=\"416.1614 398.3563 416.1614 380.5512 416.1614 380.5512 398.3563 398.3563 398.3563 380.5512 416.1614 380.5512 380.5512 398.3563 398.3563 398.3563 398.3563 398.3563 416.1614 398.3563\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "size = 150 # change the size of the page\n",
    "d = document(size, size, 'mm')\n",
    "page = d.addpage()\n",
    "figure = shape().stroke(rgba(0, 0, 0, 255)).width(2).join('round')\n",
    "grid_n = 8 # change the number of elements in the grid on one side\n",
    "grid_size = size / grid_n\n",
    "for i in range(grid_n):\n",
    "    for j in range(grid_n):\n",
    "        char_pline = make_char()\n",
    "        lines = figure.polyline(\n",
    "            char_pline.scale(grid_size * 0.67).translate(3+i*grid_size, 3+j*grid_size))\n",
    "        page.place(lines)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we're getting somewhere. When your sci-fi author friend texts you and says \"Hey, I need something that looks like a writing system for space aliens for the cover of my next book,\" you've got something all ready to go.\n",
    "\n",
    "> Exercise: Can you make these polylines fall on a 4x4 grid instead of a 3x3 grid? Or a 5x5 grid?\n",
    "\n",
    "> Exercise: Add some randomness to each point's placement, so not all points fall directly on the grid.\n",
    "\n",
    "> Exercise: Change the aspect ratio of the \"characters\"—make them wider than they are tall, or taller than they are wide."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpolating curves\n",
    "\n",
    "Due to certain properties of human physiology, handwriting hardly ever consists of exactly straight lines. To simulate the curved lines of conventional handwriting, we need to find a way to change our polylines into *curves*. One way of doing this is a [Catmull-Rom spline](https://en.wikipedia.org/wiki/Centripetal_Catmull%E2%80%93Rom_spline), which produces a sequence of [Bézier curves](https://pomax.github.io/bezierinfo/) that pass through a given set of points. Bezmerizing `Polyline` objects have a function `smooth_path()` that uses Catmull-Rom to produce a path (i.e., a sequence of drawing instructions) that can draw such a curve given a set of points.\n",
    "\n",
    "The following cell generates some points with a normal distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {},
   "outputs": [],
   "source": [
    "pts = []\n",
    "for i in range(10):\n",
    "    pts.append([normal(50, 25), normal(50, 25)])\n",
    "pline = Polyline(pts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then this cell calls `smooth_point_path()` on the points, returning a list of curves:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {},
   "outputs": [],
   "source": [
    "curve_path = pline.smooth_path()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The object returned from `.smooth_path()` is a Bezmerizing `Path` object, that contains a series of Flat \"path commands\" to draw the curve:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Path([moveto(x=43.0371, y=60.4197), curveto(x1=37.9087, y1=51.3734, x2=39.5553, y2=60.2486, x=41.0211, y=58.8882), moveto(x=41.0211, y=58.8882), curveto(x1=42.4869, y1=57.5277, x2=51.8235, y2=55.8436, x=51.8319, y=52.2570), moveto(x=51.8319, y=52.2570), curveto(x1=51.8404, y1=48.6704, x2=38.5328, y2=29.3988, x=41.0720, y=37.3685), moveto(x=41.0720, y=37.3685), curveto(x1=43.6112, y1=45.3382, x2=68.3098, y2=97.2273, x=67.0672, y=100.0751), moveto(x=67.0672, y=100.0751), curveto(x1=65.8246, y1=102.9228, x2=31.2320, y2=66.8422, x=33.6165, y=54.4552), moveto(x=33.6165, y=54.4552), curveto(x1=36.0009, y1=42.0681, x2=75.1554, y2=23.7949, x=81.3740, y=25.7530), moveto(x=81.3740, y=25.7530), curveto(x1=87.5925, y1=27.7112, x2=69.2115, y2=72.6404, x=70.9279, y=66.2040)])"
      ]
     },
     "execution_count": 275,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "curve_path"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Like `Polyline` objects, `Path`s can be translated, rotated, scaled, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For our purpose, the exact nature of Bézier curves and the Flat library's path commands are not consequential. Suffice it to say that you can pass the result of `.smooth_path()` to the `.path()` method of a flat `shape` object. The cell below draws both the points and the curve passing through those points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"283.4646pt\" version=\"1.1\" viewBox=\"0 0 283.4646 283.4646\" width=\"283.4646pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<polyline fill=\"none\" points=\"203.5019 320.7856 121.9948 171.2686 116.2802 166.9271 146.9252 148.13 116.4245 105.9265 190.1117 283.6774 95.2908 154.3611 230.6664 73.0007 201.0556 187.665 259.8591 -36.4683\" stroke=\"rgba(0,0,255,0.502)\" stroke-miterlimit=\"10\"/>\n",
       "<path d=\"M121.9948,171.2686 C107.4579,145.6255,112.1252,170.7836,116.2802,166.9271 M116.2802,166.9271 C120.4353,163.0707,146.9011,158.2968,146.9252,148.13 M146.9252,148.13 C146.9492,137.9632,109.2268,83.3353,116.4245,105.9265 M116.4245,105.9265 C123.6223,128.5177,193.634,275.605,190.1117,283.6774 M190.1117,283.6774 C186.5895,291.7498,88.5317,189.4738,95.2908,154.3611 M95.2908,154.3611 C102.0499,119.2483,213.0389,67.4501,230.6664,73.0007 M230.6664,73.0007 C248.2938,78.5514,196.1901,205.9098,201.0556,187.665\" fill=\"none\" stroke=\"rgba(255,0,0,1)\" stroke-miterlimit=\"10\" stroke-width=\"4\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(100, 100, 'mm')\n",
    "page = d.addpage()\n",
    "line_figure = shape().stroke(rgba(0, 0, 255, 128)).width(1)\n",
    "curve_figure = shape().stroke(rgba(255, 0, 0, 255)).width(4)\n",
    "lines = line_figure.polyline(pline)\n",
    "curve = curve_figure.path(curve_path)\n",
    "page.place(lines)\n",
    "page.place(curve)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You'll notice in the above example that the Catmull-Rom spline algorithm \"eats\" the first and last points of the polyline. (It uses those points to determine the position of the control points of the first and last curves of the spline.) Keep this in mind when you're using `.smooth_path()` and related functions—your procedure to generate glyphs needs to generate two extra points!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following example copies the grid of alien letterforms above, but uses `.smooth_path()` to convert the points to curves before drawing. The results are much more \"organic\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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       "<title>Untitled</title>\n",
       "<path d=\"M32.2441,32.2441 C34.2224,36.2008,34.2224,32.2441,32.2441,32.2441 M32.2441,32.2441 C30.2657,32.2441,22.3524,36.2008,20.374,32.2441 M20.374,32.2441 C18.3957,28.2874,20.374,8.5039,20.374,8.5039 M20.374,8.5039 C20.374,8.5039,22.3524,32.2441,20.374,32.2441 M20.374,32.2441 C18.3957,32.2441,8.5039,12.4606,8.5039,8.5039 M8.5039,8.5039 C8.5039,4.5472,18.3957,8.5039,20.374,8.5039 M20.374,8.5039 C22.3524,8.5039,22.3524,8.5039,20.374,8.5039\" fill=\"none\" stroke=\"rgba(0,0,0,1)\" stroke-linejoin=\"round\" stroke-width=\"2\"/>\n",
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       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "size = 100\n",
    "d = document(size, size, 'mm')\n",
    "page = d.addpage()\n",
    "figure = shape().stroke(rgba(0, 0, 0, 255)).width(2).join('round')\n",
    "grid_n = 8\n",
    "grid_size = size / grid_n\n",
    "for i in range(grid_n):\n",
    "    for j in range(grid_n):\n",
    "        char_pline = make_char()\n",
    "        char_path = char_pline.smooth_path()\n",
    "        curve = figure.path(\n",
    "            char_path.scale(grid_size*0.67).translate(3+i*grid_size, 3+j*grid_size))\n",
    "        page.place(curve)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scribbling in a line\n",
    "\n",
    "Writing in certain alphabets proceeds in a linear direction across the page with connected letters; English cursive does this in particular. To simulate this, I wrote a function that generates a polyline with random points evenly spaced along a line horizontally, with the y-coordinate of each point set according to a random number selected from a normal distribution centered on zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_scribble(width, height, steps, stddev=0):\n",
    "    pts = []\n",
    "    for i in range(steps):\n",
    "        x = ((width / steps) * i) + normal(0, stddev)\n",
    "        y = normal(0, height)\n",
    "        pts.append([x, y])\n",
    "    return Polyline(pts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what it looks like. (The green line is the original polyline; the black line is the smoothed curve.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<title>Untitled</title>\n",
       "<path d=\"M48.7559,52.8111 C55.5591,55.2526,62.3622,77.7055,69.1654,78.3249 M69.1654,78.3249 C75.9685,78.9443,82.7717,59.2148,89.5748,56.5276 M89.5748,56.5276 C96.378,53.8404,103.1811,59.8895,109.9843,62.2017 M109.9843,62.2017 C116.7874,64.5138,123.5906,67.0384,130.3937,70.4005 M130.3937,70.4005 C137.1969,73.7627,144,83.8462,150.8031,82.3748 M150.8031,82.3748 C157.6063,80.9034,164.4094,62.7743,171.2126,61.572 M171.2126,61.572 C178.0157,60.3697,184.8189,75.5678,191.622,75.1611 M191.622,75.1611 C198.4252,74.7543,205.2283,61.4457,212.0315,59.1316 M212.0315,59.1316 C218.8346,56.8176,225.6378,62.3342,232.4409,61.2767 M232.4409,61.2767 C239.2441,60.2192,246.0472,50.1956,252.8504,52.7867 M252.8504,52.7867 C259.6535,55.3778,266.4567,72.5665,273.2598,76.8234 M273.2598,76.8234 C280.063,81.0803,286.8661,81.2385,293.6693,78.3281 M293.6693,78.3281 C300.4724,75.4177,307.2756,60.769,314.0787,59.3612 M314.0787,59.3612 C320.8819,57.9533,327.685,65.7697,334.4882,69.881 M334.4882,69.881 C341.2913,73.9923,348.0945,84.4604,354.8976,84.029 M354.8976,84.029 C361.7008,83.5975,368.5039,67.7877,375.3071,67.2923 M375.3071,67.2923 C382.1102,66.7969,388.9134,81.0445,395.7165,81.0564 M395.7165,81.0564 C402.5197,81.0683,409.3228,67.3203,416.126,67.3637 M416.126,67.3637 C422.9291,67.407,429.7323,81.3644,436.5354,81.3163 M436.5354,81.3163 C443.3386,81.2682,450.1417,69.7128,456.9449,67.0749 M456.9449,67.0749 C463.748,64.4369,470.5512,67.642,477.3543,65.4886 M477.3543,65.4886 C484.1575,63.3352,490.9606,49.6129,497.7638,54.1545\" fill=\"none\" stroke=\"rgba(0,0,0,0.8627)\" stroke-miterlimit=\"10\" stroke-width=\"2\"/>\n",
       "<polyline fill=\"none\" points=\"28.3465 63.6758 48.7559 52.8111 69.1654 78.3249 89.5748 56.5276 109.9843 62.2017 130.3937 70.4005 150.8031 82.3748 171.2126 61.572 191.622 75.1611 212.0315 59.1316 232.4409 61.2767 252.8504 52.7867 273.2598 76.8234 293.6693 78.3281 314.0787 59.3612 334.4882 69.881 354.8976 84.029 375.3071 67.2923 395.7165 81.0564 416.126 67.3637 436.5354 81.3163 456.9449 67.0749 477.3543 65.4886 497.7638 54.1545 518.1732 92.738\" stroke=\"rgba(0,255,0,0.8627)\" stroke-miterlimit=\"10\" stroke-width=\"2\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "size = 200\n",
    "d = document(200, 50, 'mm')\n",
    "page = d.addpage()\n",
    "line_figure = shape().stroke(rgba(0, 255, 0, 220)).width(2)\n",
    "curve_figure = shape().stroke(rgba(0, 0, 0, 220)).width(2)\n",
    "scribble_poly = make_scribble(width=180,\n",
    "                    height=5,\n",
    "                    steps=25,\n",
    "                    stddev=0)\n",
    "lines = line_figure.polyline(scribble_poly.translate(10, 25))\n",
    "curve = curve_figure.path(scribble_poly.smooth_path().translate(10, 25))\n",
    "page.place(curve) # comment to hide curves\n",
    "page.place(lines) # comment to hide non-smooth lines\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function also has a `stddev` parameter that allows you to adjust the standard deviation of a normally-distributed random number that adjusts the spacing of each point along the x-axis. This allows for the possibility of letters looping back on themselves:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"141.7323pt\" version=\"1.1\" viewBox=\"0 0 566.9291 141.7323\" width=\"566.9291pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<path d=\"M29.4152,77.6779 C31.3611,76.0203,38.1759,76.4337,42.1748,71.7588 M42.1748,71.7588 C46.1737,67.0838,53.0827,48.7044,53.4087,49.6282 M53.4087,49.6282 C53.7348,50.552,42.1856,68.9176,44.1309,77.3014 M44.1309,77.3014 C46.0761,85.6851,61.4098,100.4852,65.0801,99.9307 M65.0801,99.9307 C68.7505,99.3762,65.1262,78.226,66.1529,73.9746 M66.1529,73.9746 C67.1797,69.7231,70.6122,75.8429,71.2405,74.422 M71.2405,74.422 C71.8689,73.001,69.1464,65.4843,69.923,65.4488 M69.923,65.4488 C70.6995,65.4134,75.7319,74.1794,75.8998,74.2093 M75.8998,74.2093 C76.0678,74.2391,69.1659,71.554,70.9308,65.6279 M70.9308,65.6279 C72.6957,59.7018,83.8496,40.0659,86.4892,38.6526 M86.4892,38.6526 C89.1288,37.2393,84.2311,51.8294,86.7683,57.1481 M86.7683,57.1481 C89.3056,62.4668,100.6986,64.7246,101.7129,70.5649 M101.7129,70.5649 C102.7272,76.4051,92.7845,93.5041,92.854,92.1896 M92.854,92.1896 C92.9236,90.8751,98.971,65.3365,102.1301,62.6777 M102.1301,62.6777 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       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "size = 200\n",
    "d = document(200, 50, 'mm')\n",
    "page = d.addpage()\n",
    "line_figure = shape().stroke(rgba(0, 255, 0, 255)).width(1)\n",
    "scribble_poly = make_scribble(width=180,\n",
    "                    height=5,\n",
    "                    steps=100,\n",
    "                    stddev=3)\n",
    "curve = curve_figure.path(scribble_poly.smooth_path().translate(10, 25))\n",
    "page.place(curve)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following example displays multiple \"lines\" of these scribbles, moving down the page, using a `for` loop:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"566.9291pt\" version=\"1.1\" viewBox=\"0 0 566.9291 566.9291\" width=\"566.9291pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<path d=\"M29.6946,24.0239 C30.1242,22.7474,31.7341,24.3025,32.8123,24.6734 M32.8123,24.6734 C33.8904,25.0443,35.4648,25.5282,36.1635,26.2495 M36.1635,26.2495 C36.8622,26.9707,36.1646,29.3632,37.0042,29.0008 M37.0042,29.0008 C37.8438,28.6383,40.0746,23.4341,41.2011,24.0748 M41.2011,24.0748 C42.3275,24.7154,43.1428,32.5815,43.7629,32.8448 M43.7629,32.8448 C44.383,33.1082,43.4329,27.6521,44.9218,25.6548 M44.9218,25.6548 C46.4106,23.6575,51.8279,20.8106,52.6961,20.861 M52.6961,20.861 C53.5643,20.9114,49.8572,26.7274,50.1308,25.9572 M50.1308,25.9572 C50.4043,25.187,52.6987,15.8484,54.3372,16.24 M54.3372,16.24 C55.9757,16.6316,59.0225,27.1264,59.9617,28.3069 M59.9617,28.3069 C60.9008,29.4874,59.3725,21.2187,59.9722,23.3229 M59.9722,23.3229 C60.5719,25.4272,61.8099,39.9025,63.5598,40.9323 M63.5598,40.9323 C65.3097,41.9622,70.2858,29.1007,70.4717,29.5022 M70.4717,29.5022 C70.6576,29.9037,65.1971,43.1779,64.6753,43.3414 M64.6753,43.3414 C64.1535,43.5049,66.9148,31.888,67.341,30.4832 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       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "size = 200\n",
    "d = document(size, size, 'mm')\n",
    "page = d.addpage()\n",
    "line_figure = shape().stroke(rgba(0, 255, 0, 255)).width(1)\n",
    "curve_figure = shape().stroke(rgba(0, 0, 0, 255)).width(2)\n",
    "row_n = 16\n",
    "for i in range(row_n):\n",
    "    scribble_poly = make_scribble(\n",
    "                        width=size-20,\n",
    "                        height=(size/row_n)*0.25,\n",
    "                        steps=int(uniform(25, 250)),\n",
    "                        stddev=uniform(2))\n",
    "    scribble_poly_tr = scribble_poly.translate(\n",
    "        10, 10 + (i*size/(row_n+1))) # row_n + 1 to leave some space at the bottom\n",
    "    lines = line_figure.polyline(scribble_poly_tr)\n",
    "    curve = curve_figure.path(scribble_poly_tr.smooth_path())\n",
    "    page.place(curve)\n",
    "    #page.place(lines) # uncomment to see original lines\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Exercise: Use the `i` parameter of the loop to control some other aspect of the line generation. (For example, make it so the number of steps increases as the scribbles move down the page.)\n",
    "\n",
    "> Exercise: Introduce randomly-placed crosses (like the cross in `t`) and dots (as in `i`)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Weighted strokes\n",
    "\n",
    "The strokes produced by the flat library have a uniform width and texture, which makes the resulting artifacts resemble drawings made with a very precise pen. The problem of how to simulate how different writing implements make marks on a page (\"brushes\" in a tool like PhotoShop) is an open area of research in computer graphics research. ([A recent review](https://onlinelibrary.wiley.com/doi/full/10.1002/cav.1435).)\n",
    "\n",
    "The Bezmerizing library implements a simple technique for simulating an ink brush or other kinds of pens, which works by drawing a polygon along the tangents of the curves composing the stroke. The `Polyline` object has a `.fancy_curve()` method that performs the technique. To demonstrate, let's create a `Polyline` object with a set of points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {},
   "outputs": [],
   "source": [
    "pline = Polyline([[10, 10], [15, 15], [15, 85], [50, 50], [85, 85], [85, 15], [90, 10]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "... and then create the polygon around the curve with `.fancy_curve()`. The `samples_per` parameter controls the resolution of the polygon (lower values are faster to calculate but chunkier) and the `thicknesses` parameter controls the thickness of the polygon along the path."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {},
   "outputs": [],
   "source": [
    "curve_poly = pline.fancy_curve(samples_per=24, thicknesses=[0, 2, 10, 2, 8, 2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's an example that draws the original polyline, the Catmull-Rom curve created from the polyline, and the simulated brushstroke, just to show you how it works:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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       "<title>Untitled</title>\n",
       "<polygon fill=\"rgba(0,0,0,0.9412)\" points=\"42.5197 42.5197 42.8611 47.7491 42.9893 54.1283 42.932 61.5332 42.7173 69.8427 42.3732 78.9367 41.9278 88.6954 41.409 98.9995 40.8449 109.7294 40.2635 120.7658 39.6928 131.9891 39.1607 143.2797 38.6952 154.5177 38.3243 165.5829 38.0758 176.3545 37.9776 186.711 38.0572 196.5298 38.3417 205.6859 38.8572 214.0508 39.6274 221.4897 41.1102 227.776 42.8419 232.7223 44.7035 236.0182 46.212 237.2526 46.634 236.8306 46.6171 236.202 46.1117 235.558 46.8223 234.591 48.6534 232.5536 51.185 229.3726 54.185 225.1772 57.5346 220.1178 61.1645 214.3376 65.0283 207.9712 69.0913 201.1469 73.3252 193.9882 77.7066 186.6148 82.2164 179.1423 86.8403 171.6824 92.5193 165.0659 98.2631 158.7243 104.063 152.7756 109.921 147.3356 115.8573 142.5207 121.9204 138.4561 128.1988 135.3017 134.8045 133.3146 141.7323 132.93 141.7323 133.5267 148.1792 135.0391 153.9034 137.9564 159.1239 141.8609 164.0643 146.5573 168.8603 151.9355 173.5798 157.9031 178.2514 164.3657 182.8823 171.223 187.4673 178.3692 192.8471 185.0915 198.1639 191.8959 203.3897 198.6544 208.4954 205.2376 213.4498 211.5139 218.2176 217.3482 222.7569 222.5992 227.0108 227.1152 230.892 230.7276 234.2402 233.243 236.7157 234.4611 237.5978 234.3899 236.2345 234.0497 234.5097 234.5097 234.1932 234.1932 233.9482 233.6342 234.4605 230.9382 235.0105 226.4672 235.3832 220.5694 236.4174 213.5447 237.2188 205.464 237.7986 196.5071 238.1775 186.829 238.3801 176.5712 238.4327 165.8672 238.3625 154.8459 238.1972 143.633 237.9647 132.3524 237.6927 121.1266 237.4095 110.0768 237.1429 99.3238 236.921 88.9876 236.772 79.1876 236.724 70.0426 236.8053 61.6704 237.0444 54.187 237.4708 47.7056 238.1165 42.3311 243.7732 42.7082 244.0346 47.7969 244.5029 54.0593 245.1544 61.3631 245.9625 69.5835 246.9 78.5992 247.9392 88.2902 249.0523 98.5376 250.2116 109.2232 251.3891 120.2295 252.5569 131.4394 253.6873 142.7368 254.7521 154.0063 255.7234 165.1343 256.5728 176.0087 257.2716 186.5209 257.7903 196.5667 258.0975 206.0501 258.158 214.8882 257.9272 223.0234 256.4546 230.2889 254.5234 236.7469 251.8626 242.508 247.6965 247.6965 247.3801 247.3801 240.9747 250.6941 234.2296 250.4517 229.0776 247.9668 224.9155 244.5044 221.0717 240.317 217.2553 235.449 213.355 229.9516 209.3323 223.9008 205.1794 217.3896 200.9032 210.5213 196.5173 203.4054 192.0396 196.1549 187.4898 188.8851 182.8888 181.7126 177.4278 175.388 171.9964 169.4431 166.6383 164.0168 161.4096 159.2535 156.3879 155.3032 151.69 152.3184 147.5005 150.4334 144.0919 149.6975 141.7323 149.9378 141.7323 150.5346 139.8535 151.422 137.3264 153.088 134.1949 155.7231 130.6197 159.3398 126.7383 163.8533 122.6481 169.1444 118.4183 175.0846 114.0998 181.5451 109.7327 188.3994 104.3759 194.8343 99.019 201.436 93.6969 208.0715 88.4393 214.612 83.2716 220.9323 78.2148 226.9115 73.2827 232.433 68.478 237.3871 63.7805 241.672 59.12 245.1938 54.3136 247.8369 48.99 249.2835 43.1028 248.5418 38.4054 245.0592 38.8274 244.6372 36.4148 240.124 35.1033 234.9628 34.3538 228.9801 33.9914 222.1031 33.4965 214.3821 33.2712 205.8282 33.2831 196.544 33.5024 186.6388 33.9005 176.2254 34.4488 165.4186 35.1193 154.3345 35.8839 143.0901 36.7148 131.8028 37.5838 120.5903 38.4632 109.5706 39.3249 98.8619 40.1411 88.5823 40.8838 78.8501 41.5253 69.7835 42.0375 61.5003 42.3926 54.1181 42.5627 47.7533 42.5197 42.5197\"/>\n",
       "<path d=\"M42.5197,42.5197 C44.8819,77.9528,25.9843,224.4094,42.5197,240.9449 M42.5197,240.9449 C59.0551,257.4803,108.6614,141.7323,141.7323,141.7323 M141.7323,141.7323 C174.8031,141.7323,224.4094,257.4803,240.9449,240.9449 M240.9449,240.9449 C257.4803,224.4094,238.5827,77.9528,240.9449,42.5197\" fill=\"none\" stroke=\"rgba(0,255,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "<polyline fill=\"none\" points=\"28.3465 28.3465 42.5197 42.5197 42.5197 240.9449 141.7323 141.7323 240.9449 240.9449 240.9449 42.5197 255.1181 28.3465\" stroke=\"rgba(255,0,0,1)\" stroke-miterlimit=\"10\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(100, 100, 'mm')\n",
    "page = d.addpage()\n",
    "curve_figure = shape().nostroke().fill(rgba(0, 0, 0, 240))\n",
    "smooth_figure = shape().stroke(rgba(0, 255, 0, 255))\n",
    "poly_figure = shape().stroke(rgba(255, 0, 0, 255))\n",
    "smooth_path = pline.smooth_path()\n",
    "fancy_poly = curve_figure.polygon(curve_poly)\n",
    "path = smooth_figure.path(smooth_path)\n",
    "poly = poly_figure.polyline(pline)\n",
    "page.place(fancy_poly)\n",
    "page.place(path)\n",
    "page.place(poly)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the \"alien characters\" example above, except using `fancy_curve()` to generate polygons for each stroke. (Try playing around with the `thickness` parameter.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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       "<title>Untitled</title>\n",
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       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "size = 150\n",
    "d = document(size, size, 'mm')\n",
    "page = d.addpage()\n",
    "figure = shape().nostroke().fill(rgba(0, 0, 0, 255))\n",
    "grid_n = 8\n",
    "grid_size = size / grid_n\n",
    "for i in range(grid_n):\n",
    "    for j in range(grid_n):\n",
    "        char_pline = make_char().scale(grid_size * 0.67).translate(3 + i * grid_size, 3 + j * grid_size)\n",
    "        poly = char_pline.fancy_curve(samples_per=12, thicknesses=[3, 1, 1, 2], tightness=-0.25)\n",
    "        poly = figure.polygon(poly)\n",
    "        page.place(poly)\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Connecting polylines\n",
    "\n",
    "`Polyline` objects can be added together, creating a new polyline that combines their points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 352,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Polyline([[10.0000, 10.0000], [20.0000, 20.0000], [25.0000, 35.0000], [20.0000, 25.0000]])"
      ]
     },
     "execution_count": 352,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = Polyline([[10, 10], [20, 20]])\n",
    "b = Polyline([[25, 35], [20, 25]])\n",
    "a + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use this feature to combine two glyphs from the `make_char()` function, translating the second glyph to be to the right of the first glyph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 370,
   "metadata": {},
   "outputs": [],
   "source": [
    "composite = make_char() + make_char().translate(1.5, 0)\n",
    "composite = composite.scale(30).translate(10, 10) # scale it up so we can actually see it!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what it looks like (original polyline in light purple, curve in cyan):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 375,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg height=\"141.7323pt\" version=\"1.1\" viewBox=\"0 0 283.4646 141.7323\" width=\"283.4646pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<title>Untitled</title>\n",
       "<polyline fill=\"none\" points=\"70.8661 113.3858 28.3465 70.8661 70.8661 113.3858 70.8661 28.3465 113.3858 28.3465 28.3465 113.3858 28.3465 70.8661 70.8661 28.3465 70.8661 70.8661 155.9055 70.8661 155.9055 113.3858 198.4252 70.8661 155.9055 70.8661 155.9055 28.3465 240.9449 113.3858 198.4252 113.3858 198.4252 70.8661 198.4252 28.3465 155.9055 70.8661\" stroke=\"rgba(160,80,160,1)\" stroke-miterlimit=\"10\"/>\n",
       "<path d=\"M28.3465,70.8661 C28.3465,70.8661,63.7795,120.4724,70.8661,113.3858 M70.8661,113.3858 C77.9528,106.2992,63.7795,42.5197,70.8661,28.3465 M70.8661,28.3465 C77.9528,14.1732,120.4724,14.1732,113.3858,28.3465 M113.3858,28.3465 C106.2992,42.5197,42.5197,106.2992,28.3465,113.3858 M28.3465,113.3858 C14.1732,120.4724,21.2598,85.0394,28.3465,70.8661 M28.3465,70.8661 C35.4331,56.6929,63.7795,28.3465,70.8661,28.3465 M70.8661,28.3465 C77.9528,28.3465,56.6929,63.7795,70.8661,70.8661 M70.8661,70.8661 C85.0394,77.9528,141.7323,63.7795,155.9055,70.8661 M155.9055,70.8661 C170.0787,77.9528,148.8189,113.3858,155.9055,113.3858 M155.9055,113.3858 C162.9921,113.3858,198.4252,77.9528,198.4252,70.8661 M198.4252,70.8661 C198.4252,63.7795,162.9921,77.9528,155.9055,70.8661 M155.9055,70.8661 C148.8189,63.7795,141.7323,21.2598,155.9055,28.3465 M155.9055,28.3465 C170.0787,35.4331,233.8583,99.2126,240.9449,113.3858 M240.9449,113.3858 C248.0315,127.5591,205.5118,120.4724,198.4252,113.3858 M198.4252,113.3858 C191.3386,106.2992,198.4252,85.0394,198.4252,70.8661 M198.4252,70.8661 C198.4252,56.6929,205.5118,28.3465,198.4252,28.3465\" fill=\"none\" stroke=\"rgba(0,128,128,1)\" stroke-miterlimit=\"10\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(100, 50, 'mm')\n",
    "page = d.addpage()\n",
    "line_fig = shape().stroke(rgba(160, 80, 160, 255)).nofill()\n",
    "curve_fig = shape().stroke(rgba(0, 128, 128, 255)).nofill()\n",
    "page.place(line_fig.polyline(composite))\n",
    "page.place(curve_fig.path(composite.smooth_path()))\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make a whole row of these, just keep appending glyphs with increasing translation along the X axis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 386,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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       "<title>Untitled</title>\n",
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       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "line = make_char()\n",
    "for i in range(1, 10):\n",
    "    line += make_char().translate(i*1.5, 0)\n",
    "line = line.scale(10).translate(10, 10)\n",
    "d = document(200, 30, 'mm')\n",
    "page = d.addpage()\n",
    "line_fig = shape().stroke(rgba(160, 80, 160, 255)).nofill()\n",
    "curve_fig = shape().stroke(rgba(0, 128, 128, 255)).nofill()\n",
    "page.place(line_fig.polyline(line))\n",
    "page.place(curve_fig.path(line.smooth_path()))\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following example takes advantage of this technique in order to produce a composition of several lines. As a change of pace, let's work with a limited set of glyphs, instead of generating a new glyph every time we want to place one on the page:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 395,
   "metadata": {},
   "outputs": [],
   "source": [
    "chars = [make_char() for i in range(26)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Working with a limited set of glyphs (in my experience) provides a bit of verisimilitude, since you expect to see repeated figures in handwriting. But you also have to be careful to add a bit of variation to the glyphs, because otherwise it can look a bit \"robotic.\" (Though \"robotic\" might be exactly what you're going for. I don't know.)\n",
    "\n",
    "The code below generates ten lines of these \"cursive\" (i.e., connected) forms:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 398,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<title>Untitled</title>\n",
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       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = document(150, 150, 'mm')\n",
    "page = d.addpage()\n",
    "line_fig = shape().stroke(rgba(128, 0, 128, 255)).nofill()\n",
    "curve_fig = shape().stroke(rgba(0, 128, 128, 255)).nofill()\n",
    "for row in range(10):\n",
    "    line = choice(chars)\n",
    "    for col in range(1, 10):\n",
    "        # scale(normal(...)) adds a bit of size variation to the glyphs\n",
    "        line += choice(chars).scale(normal(1, 0.25)).translate(col*1.5, 0)\n",
    "    # translate the row to the right place on the screen and make it bigger\n",
    "    line = line.translate(1, 1+row*1.5).scale(9)\n",
    "    smooth = line.smooth_path()\n",
    "    #page.place(line_fig.polyline(line)) # uncomment to see original polylines\n",
    "    page.place(curve_fig.path(smooth))\n",
    "show(page)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
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